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Early experiences with DWF on
QCDOC
This is a physics talk
Only possible due to a huge amount of work from
all the people on the QCDOC project
Physics contributions from many RBC and UKQCD people
All results are very preliminary
Chris Maynard
RBC-UKQCD
March 2005
ILFT2 Edinburgh
1
Introduction
Chirally symmetric fermions
– Domain Wall fermions (DWF)
Kaplan 92, Shamir 93,
Furman-Shamir 95
Both chiral and flavour symmetry at finite a
– Continuum-like chiral perturbation theory
– No flavour mixing, “wrong chirality” operating
mixing small
Dynamical DWF is QFT
Computationally expensive
Residual chiral symmetry breaking mres
March 2005
ILFT2 Edinburgh
2
Outline
Chiral symmetry breaking – mres
Preliminary results (statistics limited) for
– The effect of the gauge action on mres
• Valence M5 and LS. The potential
– The effect of the gauge coupling on mres
– The effect of the quark mass on mres
– The effect of LS on mres
Other talks
– Algorithm (MAC) and Machine (PAB)
Summary and outlook
March 2005
ILFT2 Edinburgh
3
Chiral symmetry breaking and mres
4d quark field constructed from left (right)
projections of
on boundary
Quark mass is
LS not infinite L-R coupling
Define J5 current in terms of fields at LS/2 - (1,LS)
Axial Ward-Takahashi Identity and thus mres
March 2005
ILFT2 Edinburgh
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Small is beautiful
How to reduce chiral symmetry breaking
Desire mres as small as possible
– LS infinity is expensive
– Overlap: Ultimate operator. Expensive
– See BJ talk GWF and cost
• We are keen to adopt these improvements
How do simulation parameters effect mres
– Gauge action, M5, LS, gauge coupling mf
– Inform decision on “Big Run”
March 2005
ILFT2 Edinburgh
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Gauge Action
Measure dependence
of mres on rectangle
term
Quenched studies
show lines of constant
a approx quadratic in
b,|c1|/|1-8c1| plane
Zoom in to top left
Keep a constant vary c1
and b
March 2005
ILFT2 Edinburgh
6
Ensembles RBC
Nf=3 amf=0.04, t=0.5 dt =0.01 aM5=1.8
b
c1 Mud/ms
LS
Alg
Traj/cfg
0.72
-1.4069
1
8
R
1500 / 96
0.48
-2.300
1
8
R
1605 / 101
0.32
-3.570
1
8
R
1600 / 101
0.16
-7.470
1
8
R
1520 / 102
0.80
-1.4069
1
8
R
1900 / 126
0.53
-2.300
1
8
R
1400 / 81
March 2005
ILFT2 Edinburgh
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Residual mass
Nf = 3 amf = 0.04
LS=8 DBW2
March 2005
ILFT2 Edinburgh
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Mres versus rectangle
Increase rectange,
decrease mres
No dramatic
decrease in mres
Lattice artefacts
scaling behaviour?
Conservative opinion:
Maybe not worth it
March 2005
ILFT2 Edinburgh
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The potential
Compare lattice spacing from mr and r0
– Look for lattice artefacts
ms=0.04 mv=-mres
No sea extrapolation
No strong sea quark mass dependence
March 2005
ILFT2 Edinburgh
10
NF=2 sea quark mass dependence
March 2005
ILFT2 Edinburgh
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Scaled potential
Rescaled
potential
NF=0,NF=2
different short
distance
behaviour
No obvious
differences for c1
March 2005
ILFT2 Edinburgh
12
Lattice artefacts
Some
variation with
c1
Approx 10%
This suggests
it is not an
extreme effect
March 2005
ILFT2 Edinburgh
13
Valence LS
LSsea=8
mres decreases
as LS increases
Not exponetial
Not surprising as
PQ
Same as
quenched
March 2005
ILFT2 Edinburgh
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Ensembles UKQCD
RHMC
b
c1
Mud/ms
LS
Alg
Traj/cfg
0.72
-1.4069
1
8
R
1500 / 70
0.72
0.72
0.72
0.72
-1.4069
-1.4069
-1.4069
-1.4069
0.5
1
1
0.5
8
8
12
12
R
RHMC
RHMC
RHMC
1345 / 51
1200
<500
1200
0.72
0.88
0.88
-1.4069
-1.4069
-1.4069
0.3
1
0.5
12
8
12
RHMC
R
RHMC
<500
1500 / 75
<500
March 2005
ILFT2 Edinburgh
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mres vs mf
b = 0.72 LS = 8 R
algorithm
mval = msea
No strong mq
dependence
No fit. Straight line
through two points
March 2005
ILFT2 Edinburgh
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(amPS)2 vs amq
Intercept not
equal to mres
Straight line
through two
points
Autocorrelation?
Statistics (50)
March 2005
ILFT2 Edinburgh
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amr vs amq
msea = mval
Straight line
through two
points
amr at
mq = - mres
a-1 = 1.4(3) GeV
March 2005
ILFT2 Edinburgh
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amr vs amf valence
Valence only
extrapolation
a-1 ~ 1.45 GeV
March 2005
ILFT2 Edinburgh
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mres vs a2
Lattice spacing
PQ r mass
mres PQ
extrapolation
Sea quark mass
not same
Approx
exponential
behaviour
March 2005
ILFT2 Edinburgh
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Summary and Outlook
First physics from QCDOC!
– Very preliminary
We are exploring the effects of simulation
parameters on residual chiral symmetry
breaking
Accumulating more data
Some conclusions soon!
March 2005
ILFT2 Edinburgh
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